Finite Group DatabasebetaFinite Group DatabasebetaOrder 24704.
828 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 280 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C193 | C23 |
| commutator | C22 | C2×C42×C193 |
| Frattini, cosocle | C24 | C23×C193 |
| prime radical | C25×C193 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C193 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C42×C193 | C2 | semidirect |
| 3. C2×#95×C193 | C2 | semidirect |
| 9. C2×C22⋊C4×C193 | C4 | semidirect |
| 39. C23×C193 | C42 | semidirect |
| 53. C2×C4×C193 | C22⋊C4 | semidirect |
| 76. C193 | #1437 | direct (N × H) |
| 77. #1437 | C193 | direct (N × H) |
| 79. C22×C42 | C2×C193 | semidirect |
| 80. C2×#95 | C2×C193 | semidirect |
| 86. C2×C22⋊C4 | C4×C193 | semidirect |
| 116. C23 | C42×C193 | semidirect |
| 130. C2×C4 | C22⋊C4×C193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊C4×C193 | 2 |
| C22×C42×C193 | 2 |
| C2×#95×C193 | 2 |
| #1437 | 193 |